We did fine with this 3d party site:
https://www.st-marks-basilica.com/
Only the 9:30 timed entry slot was available, and only rhe basic visit Basilica floor lap only) but we were able to pay €7 each once inside and go upstairs to see the museum, the original horses, and go outside on the terrace ( these are the best part of visiting the basilica for us). The tix cost €9, €3 more than the official site, but it was worth it to be able to go inside after I waited too long to get our tickets from the official site. (A month ahead was already too late).
We liked the 9:30 time as we were the first ones in the museum and had the four horses all to ourselves for a good 10 minutes.